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Mirrors > Home > NFE Home > Th. List > ax12b | Unicode version |
Description: Two equivalent ways of expressing ax-12 1925. See the comment for ax-12 1925. (Contributed by NM, 2-May-2017.) (Proof shortened by Wolf Lammen, 12-Aug-2017.) |
Ref | Expression |
---|---|
ax12b |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | id 19 |
. . 3
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2 | 1 | a1dd 42 |
. 2
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3 | equtrr 1683 |
. . . . . 6
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4 | 3 | equcoms 1681 |
. . . . 5
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5 | 4 | con3rr3 128 |
. . . 4
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6 | id 19 |
. . . . . 6
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7 | 6 | com4l 78 |
. . . . 5
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8 | 7 | com23 72 |
. . . 4
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9 | 5, 8 | mpdd 36 |
. . 3
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10 | 9 | com3r 73 |
. 2
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11 | 2, 10 | impbii 180 |
1
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Colors of variables: wff setvar class |
Syntax hints: ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1546 ax-5 1557 ax-17 1616 ax-9 1654 ax-8 1675 |
This theorem depends on definitions: df-bi 177 df-ex 1542 |
This theorem is referenced by: (None) |
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